You can get some of that information by querying OpenGL with glGet*(). Do 'man glGet' in the Terminal to see what information is available.

[EDIT: That wasn't strictly correct... I meant aglDescribeRenderer(). There's an example of how to use it in the old CFM OpenGL SDK. It's called 'Renderer Info'.]

[EDIT AGAIN: Since the CFM OpenGL SDK is the size of a small planet, just ask me to email the relevant source file if you're interested!]

You can query the Display Manager to discover which resolutions are available for a particular display. Some other APIs may offer easier ways to get at the same information (DrawSprocket does, for example).

I don't think there's any way to discover the fill rate of a card without running a timed test on it.